Estimating Distances from Parallaxes Bailer-Jones, Coryn A. L.
Publications of the Astronomical Society of the Pacific,
10/2015, Letnik:
127, Številka:
956
Journal Article
Recenzirano
Odprti dostop
Astrometric surveys such as Gaia and LSST will measure parallaxes for hundreds of millions of stars. Yet they will not measure a single distance. Rather, a distance must be estimated from a parallax. ...In this didactic article, I show that doing this is not trivial once the fractional parallax error is larger than about 20%, which will be the case for about 80% of stars in the Gaia catalog. Estimating distances is an inference problem in which the use of prior assumptions is unavoidable. I investigate the properties and performance of various priors and examine their implications. A supposed uninformative uniform prior in distance is shown to give very poor distance estimates (large bias and variance). Any prior with a sharp cut-off at some distance has similar problems. The choice of prior depends on the information one has available-and is willing to use-concerning, e.g., the survey and the Galaxy. I demonstrate that a simple prior which decreases asymptotically to zero at infinite distance has good performance, accommodates nonpositive parallaxes, and does not require a bias correction.
The halo of the Milky Way provides unique elemental abundance and kinematic information on the first objects to form in the Universe, and this information can be used to tightly constrain models of ...galaxy formation and evolution. Although the halo was once considered a single component, evidence for its dichotomy has slowly emerged in recent years from inspection of small samples of halo objects. Here we show that the halo is indeed clearly divisible into two broadly overlapping structural components--an inner and an outer halo--that exhibit different spatial density profiles, stellar orbits and stellar metallicities (abundances of elements heavier than helium). The inner halo has a modest net prograde rotation, whereas the outer halo exhibits a net retrograde rotation and a peak metallicity one-third that of the inner halo. These properties indicate that the individual halo components probably formed in fundamentally different ways, through successive dissipational (inner) and dissipationless (outer) mergers and tidal disruption of proto-Galactic clumps.
Celotno besedilo
Dostopno za:
DOBA, IJS, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
ABSTRACT Estimating a distance by inverting a parallax is only valid in the absence of noise. As most stars in the Gaia catalog will have non-negligible fractional parallax errors, we must treat ...distance estimation as a constrained inference problem. Here we investigate the performance of various priors for estimating distances, using a simulated Gaia catalog of one billion stars. We use three minimalist, isotropic priors, as well an anisotropic prior derived from the observability of stars in a Milky Way model. The two priors that assume a uniform distribution of stars-either in distance or in space density-give poor results: The root mean square fractional distance error, , grows far in excess of 100% once the fractional parallax error, , is larger than 0.1. A prior assuming an exponentially decreasing space density with increasing distance performs well once its single parameter-the scale length- has been set to an appropriate value: is roughly equal to for , yet does not increase further as increases up to to 1.0. The Milky Way prior performs well except toward the Galactic center, due to a mismatch with the (simulated) data. Such mismatches will be inevitable (and remain unknown) in real applications, and can produce large errors. We therefore suggest adopting the simpler exponentially decreasing space density prior, which is also less time-consuming to compute. Including Gaia photometry improves the distance estimation significantly for both the Milky Way and exponentially decreasing space density prior, yet doing so requires additional assumptions about the physical nature of stars.
ABSTRACT We infer distances and their asymmetric uncertainties for two million stars using the parallaxes published in the Gaia DR1 (GDR1) catalogue. We do this with two distance priors: A ...minimalist, isotropic prior assuming an exponentially decreasing space density with increasing distance, and an anisotropic prior derived from the observability of stars in a Milky Way model. We validate our results by comparing our distance estimates for 105 Cepheids which have more precise, independently estimated distances. For this sample we find that the Milky Way prior performs better (the rms of the scaled residuals is 0.40) than the exponentially decreasing space density prior (rms is 0.57), although for distances beyond 2 kpc the Milky Way prior performs worse, with a bias in the scaled residuals of −0.36 (versus −0.07 for the exponentially decreasing space density prior). We do not attempt to include the photometric data in GDR1 due to the lack of reliable color information. Our distance catalog is available at http://www.mpia.de/homes/calj/tgas_distances/main.html as well as at CDS. This should only be used to give individual distances. Combining data or testing models should be done with the original parallaxes, and attention paid to correlated and systematic uncertainties.
We present a machine learning package for the classification of periodic variable stars. Our package is intended to be general: it can classify any single band optical light curve comprising at least ...a few tens of observations covering durations from weeks to years with arbitrary time sampling. We use light curves of periodic variable stars taken from OGLE and EROS-2 to train the model. To make our classifier relatively survey-independent, it is trained on 16 features extracted from the light curves (e.g., period, skewness, Fourier amplitude ratio). The model classifies light curves into one of seven superclasses – δ Scuti, RR Lyrae, Cepheid, Type II Cepheid, eclipsing binary, long-period variable, non-variable – as well as subclasses of these, such as ab, c, d, and e types for RR Lyraes. When trained to give only superclasses, our model achieves 0.98 for both recall and precision as measured on an independent validation dataset (on a scale of 0 to 1). When trained to give subclasses, it achieves 0.81 for both recall and precision. The majority of misclassifications of the subclass model is caused by confusion within a superclass rather than between superclasses. To assess classification performance of the subclass model, we applied it to the MACHO, LINEAR, and ASAS periodic variables, which gave recall/precision of 0.92/0.98, 0.89/0.96, and 0.84/0.88, respectively. We also applied the subclass model to Hipparcos periodic variable stars of many other variability types that do not exist in our training set, in order to examine how much those types degrade the classification performance of our target classes. In addition, we investigate how the performance varies with the number of data points and duration of observations. We find that recall and precision do not vary significantly if there are more than 80 data points and the duration is more than a few weeks.
ABSTRACT
We construct a supervised classifier based on Gaussian Mixture Models to probabilistically classify objects in Gaia data release 2 (GDR2) using only photometric and astrometric data in that ...release. The model is trained empirically to classify objects into three classes – star, quasar, galaxy – for G ≥ 14.5 mag down to the Gaia magnitude limit of G = 21.0 mag. Galaxies and quasars are identified for the training set by a cross-match to objects with spectroscopic classifications from the Sloan Digital Sky Survey. Stars are defined directly from GDR2. When allowing for the expectation that quasars are 500 times rarer than stars, and galaxies 7500 times rarer than stars (the class imbalance problem), samples classified with a threshold probability of 0.5 are predicted to have purities of 0.43 for quasars and 0.28 for galaxies, and completenesses of 0.58 and 0.72, respectively. The purities can be increased up to 0.60 by adopting a higher threshold. Not accounting for this expected low frequency of extragalactic objects (the class prior) would give both erroneously optimistic performance predictions and severely impure samples. Applying our model to all 1.20 billion objects in GDR2 with the required features, we classify 2.3 million objects as quasars and 0.37 million objects as galaxies (with individual probabilities above 0.5). The small number of galaxies is due to the strong bias of the satellite detection algorithm and on-ground data selection against extended objects. We infer the true number of quasars and galaxies – as these classes are defined by our training set – to be 690 000 and 110 000, respectively (±50 per cent). The aim of this work is to see how well extragalactic objects can be classified using only GDR2 data. Better classifications should be possible with the low resolution spectroscopy (BP/RP) planned for GDR3.
Gaia Data Release 2 Luri, X.; Brown, A. G. A.; Sarro, L. M. ...
Astronomy and astrophysics (Berlin),
08/2018, Letnik:
616
Journal Article
Recenzirano
Odprti dostop
Context.
The second
Gaia
data release (
Gaia
DR2) provides precise five-parameter astrometric data (positions, proper motions, and parallaxes) for an unprecedented number of sources (more than 1.3 ...billion, mostly stars). This new wealth of data will enable the undertaking of statistical analysis of many astrophysical problems that were previously infeasible for lack of reliable astrometry, and in particular because of the lack of parallaxes. However, the use of this wealth of astrometric data comes with a specific challenge: how can the astrophysical parameters of interest be properly inferred from these data?
Aims.
The main focus of this paper, but not the only focus, is the issue of the estimation of distances from parallaxes, possibly combined with other information. We start with a critical review of the methods traditionally used to obtain distances from parallaxes and their shortcomings. Then we provide guidelines on how to use parallaxes more efficiently to estimate distances by using Bayesian methods. In particular we also show that negative parallaxes, or parallaxes with relatively large uncertainties still contain valuable information. Finally, we provide examples that show more generally how to use astrometric data for parameter estimation, including the combination of proper motions and parallaxes and the handling of covariances in the uncertainties.
Methods.
The paper contains examples based on simulated
Gaia
data to illustrate the problems and the solutions proposed. Furthermore, the developments and methods proposed in the paper are linked to a set of tutorials included in the
Gaia
archive documentation that provide practical examples and a good starting point for the application of the recommendations to actual problems. In all cases the source code for the analysis methods is provided.
Results.
Our main recommendation is to always treat the derivation of (astro-)physical parameters from astrometric data, in particular when parallaxes are involved, as an inference problem which should preferably be handled with a full Bayesian approach.
Conclusions.
Gaia
will provide fundamental data for many fields of astronomy. Further data releases will provide more data, and more precise data. Nevertheless, to fully use the potential it will always be necessary to pay careful attention to the statistical treatment of parallaxes and proper motions. The purpose of this paper is to help astronomers find the correct approach.
Using effective temperature and metallicity derived from SDSS spectra for image60,000 F- and G-type main-sequence stars, we develop polynomial models for estimating these parameters from the SDSS ...image and image colors. These photometric estimates have similar error properties as those determined from SDSS spectra. We apply this method to SDSS photometric data for over 2 million F/G stars and measure the unbiased metallicity distribution for a complete volume-limited sample of stars at distances between 500 pc and 8 kpc. The metallicity distribution can be exquisitely modeled using two components with a spatially varying number ratio, which correspond to disk and halo. The two components also possess the kinematics expected for disk and halo stars. The metallicity of the halo component is spatially invariant, while the median disk metallicity smoothly decreases with distance from the Galactic plane from -0.6 at 500 pc to -0.8 beyond several kiloparsecs. The absence of a correlation between metallicity and kinematics for disk stars is in a conflict with the traditional decomposition in terms of thin and thick disks. We detect coherent substructures in the kinematics-metallicity space, such as the Monoceros stream, which rotates faster than the LSR, and has a median metallicity of image, with an rms scatter of only image0.15 dex. We extrapolate our results to the performance expected from the Large Synoptic Survey Telescope (LSST) and estimate that LSST will obtain metallicity measurements accurate to 0.2 dex or better, with proper-motion measurements accurate to image0.5 mas yr super(-1), for about 200 million F/G dwarf stars within a distance limit of image100 kpc.
Direct imaging searches for exoplanets around stars detect many spurious candidates that are in fact background field stars. To help distinguish these from genuine companions, multi-epoch astrometry ...can be used to identify a common proper motion with the host star. Although this is frequently done, many approaches lack an appropriate model for the motions of the background population, or do not use a statistical framework to properly quantify the results. For this study we used Gαìα astrometry combined with 2MASS photometry to model the parallax and proper motion distributions of field stars around exoplanet host stars as a function of candidate magnitude. We developed a likelihood-based method that compares the positions of a candidate at multiple epochs with the positions expected under both this field star model and a co-moving companion model. Our method propagates the covariances in the Gαìα astrometry and the candidate positions. True companions are assumed to have long periods compared to the observational baseline, so we currently neglect orbital motion. We applied our method to a sample of 23 host stars with 263 candidates identified in the B-Star Exoplanet Abundance Study (BEAST) survey on VLT/SPHERE. We identified seven candidates in which the odds ratio favours the co-moving companion model by a factor of 100 or more. Most of these detections are based on only two or three epochs separated by less than three years, so further epochs should be obtained to reassess the companion probabilities. Our method is publicly available as an open-source python package from GitHub to use with any data.
Abstract
White dwarfs (WDs) offer unrealized potential in solving two problems in astrophysics: stellar age accuracy and precision. WD cooling ages can be inferred from surface temperatures and ...radii, which can be constrained with precision by high-quality photometry and parallaxes. Accurate and precise Gaia parallaxes along with photometric surveys provide information to derive cooling and total ages for vast numbers of WDs. Here we analyze 1372 WDs found in wide binaries with main-sequence (MS) companions and report on the cooling and total age precision attainable in these WD+MS systems. The total age of a WD can be further constrained if its original metallicity is known because the MS lifetime depends on metallicity at fixed mass, yet metallicity is unavailable via spectroscopy of the WD. We show that incorporating spectroscopic metallicity constraints from 38 wide binary MS companions substantially decreases internal uncertainties in WD total ages compared to a uniform constraint. Averaged over the 38 stars in our sample, the total (internal) age uncertainty improves from 21.04% to 16.77% when incorporating the spectroscopic constraint. Higher mass WDs yield better total age precision; for eight WDs with zero-age MS masses ≥2.0
M
⊙
, the mean uncertainty in total ages improves from 8.61% to 4.54% when incorporating spectroscopic metallicities. We find that it is often possible to achieve 5% total age precision for WDs with progenitor masses above 2.0
M
⊙
if parallaxes with ≤1% precision and Pan-STARRS
g
,
r
, and
i
photometry with ≤0.01 mag precision are available.
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